Probability

Perhaps one of most important mathematical tools that have an immense practical value and use, Probability is also one of the most dreaded subjects. Simply speaking it is a term that defines the chance of an event occurring, out of the whole spectrum of negative as well as positive occurrences. It is expressed as a ratio, between number of chances that an event will occur and total number of chances of the event happening or not happening at all. When you are considering calculation or a mathematical expression in figures of the amount of chances that an event has of occurring, there are some important terms that you should consider.

These may be of an experiment: which is essentially a situation or a happening that is not fixed or constant; and as such depends on chances: chances that it may happen or chances that it may not happen; outcome, which is result of above event after it has occurred; and in mathematical terms, may be defined as a result arising out of one single trial of a happening or an experiment. Other terms involved in Probability are event and probability itself. Event is a term given to either of two chances actually happening: that is event is an outcome that has been defined earlier; and lastly probability is a figurative expression of how many chances are there for a particular event to occur out of a total of negative and positive chances.

Thus Probability would be defined as a ratio expressed between two important values: those of total number of ways that a particular event may occur (or not occur); to the total number of outcomes that would be possible. An important point to be noted is that that lower value or denominator in above ratio is that of 1; and will always be 1. This is because mathematically, total number of possible chances that an event may occur at all (both positive and negative), is taken to be a ‘whole’ and thus would be equivalent to 1.

This may also be explained in the sense that mathematically, any whole is expressed in the form of fractions, would be such that both denominator as well as numerator would be equal in value. Hence, after reduction of any such fraction, obvious answer is one. However, above probability is a ratio of both negative and positive outcomes to total number of outcomes. Depending one the results that you get, events may be termed as being mutually exclusive or being complementary. In the former case, if either event is only possible if the other is not possible or does not happen; similarly, if two events would only occur, such that one would occur only if the other happens. The latter kind may also be termed as conditional probability. There is yet another possibility that result may be independent; this implies that two events would occur irrespective of whether or not the other is occurring. Hence, it is an important mathematical tool that you may employ in everyday life; and to everyday events; such as finance, statistics, machine-learning and artificial intelligience.